A Jose Callejon goal helped Napoli ease into the Champions League group stage on Tuesday, while Sevilla also went through and Celtic suffered a scare in Kazakhstan before winning their play-off tie.
Third in Serie A last season, Napoli were too strong for Nice, winning 2-0 in France with Callejon and Lorenzo Insigne both scoring as they progressed 4-0 on aggregate.
Beaten by eventual winners Real Madrid in the last 16 last season, Maurizio Sarri's side took the lead when Marek Hamsik deposited a low cross from the left for Callejon to convert at the back post in the 48th minute.
The dangerous Dries Mertens then hit the post before Insigne sealed the Italians' win a minute from time.
"Napoli must keep on playing in the Champions League every season, because this is where we belong. We are happy with the qualification," said Insigne.
Nice, for whom recent signing Wesley Sneijder started, were thoroughly outplayed over the two legs and will have to settle for a place in the group stage of the Europa League instead.
Sevilla, who won the Europa League three years in a row before losing to Leicester City in the last 16 of the Champions League last season, survived an almighty scare against Istanbul Basaksehir to go through.
The Spanish side, 2-1 winners in the first leg in Turkey, drew 2-2 at the Sanchez Pizjuan to advance 4-3 on aggregate.
They went behind on the night to an Eljero Elia goal but Sergio Escudero headed in a Jesus Navas cross early in the second half for the home side.
Great play from Nolito then set up Wissam Ben Yedder to seemingly end any doubt, but Edin Visca levelled the scores again on the night and an Emre Belozoglu free-kick struck the woodwork in the last minute as Sevilla came within a whisker of going out on away goals.
- 'Mixed emotions' -
Celtic went through 8-4 on aggregate despite losing 4-3 to Astana in the second leg of their play-off in Kazakhstan as a second-half wobble gave their hosts hope of pulling off a miraculous recovery.
Brendan Rodgers' side had won 5-0 in the first leg in Glasgow and a super Scott Sinclair strike in the 34th minute should have killed the tie.
Astana, who had gone ahead on the night through a Kristoffer Ajer own goal, were given something to cling onto as a goal by Serikzhan Muzhikov and a Patrick Twumasi brace made it 4-1 on the night.
But Olivier Ntcham ended Astana's hopes when his deflected strike made it 4-2 on the night before Leigh Griffiths reduced the deficit further in the final minute.
"I have mixed emotions because we didn't defend well enough," Rodgers told BT Sport after a scare that brought back memories of the same stage 12 months ago.
Celtic beat Hapoel Beer-Sheva of Israel 5-2 at home in the first leg of the play-offs last year and then wobbled in the return, losing 2-0 to scrape through.
"We had our Beer-Sheva moment. I thought we were going to get through this campaign without the anxiety. The players were on the ropes for 15 or 20 minutes but then they regained composure."
Greek champions Olympiakos are also back in the group stage following a 1-0 victory away to Croatian champions Rijeka that took them through 3-1 on aggregate. German international Marko Marin scored the only goal on the night.
Maribor of Slovenia also progressed, beating Hapoel Beer-Sheva 1-0 with a Mitja Viler strike as they won the tie on away goals.
The remaining five ties will conclude on Wednesday, with the highlight seeing Liverpool take a 2-1 lead into their play-off second leg against Hoffenheim at Anfield.
The draw for the lucrative group stage will be held in Monaco on Thursday.